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#41×D₁₁ #67041

order	352
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

#41×D₁₁

Splittings

Fitting	C₁₁×#41 ⋊ C₂
Sylow	C₁₁ ⋊ C₂×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₁₁
commutator, socle, cosocle	C₂×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₁₁
Fitting	C₁₁×#41	C₂
hypercenter	#41	D₁₁
hypocenter	C₁₁	C₂×#41
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ #41

164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 4 generators on 19 points:

(2,3)(4,5)(6,7)(8,9)(10,11);(1,2,4,6,8,10,11,9,7,5,3)(12,14,15,18)(13,17,16,19);(13,16)(17,19);(12,13)(14,17)(15,16)(18,19)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×#104, #10622434, D₁₁×#131, …
maximal normal subgroup of	D₁₁×#104, #10622434, D₁₁×#131, …
maximal quotient of	#10623048, D₁₁×#117, #10623053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 183);